Passivity‐based robust adaptive sliding mode control for singular time‐delay systems with uncertainties in both derivative matrix and some other system matrices

Abstract

This article addresses the passivity analysis and passification problems for a class of nonlinear singular time-varying delay systems with the special forms of uncertainties in both derivative matrix and some other system matrices by adopting adaptive sliding mode control (SMC) strategy. First, a distinctive state augmentation technique, which keeps the admissibility and the robust passivity unchanged, is employed due to "left-singular" form uncertainty in the derivative matrix (ie, E 0 (I + ΔE 0 ())). Next, an integral-type sliding surface, which involves the SMC gain matrix K, is constructed. By designing an appropriate Lyapunov-Krasovskii functional and introducing slack matrix approach, in which the slack matrixW is not constrained in contrast to most existing literatures, a new sufficient condition is derived to ensure that the resulting sliding mode dynamics is admissible and robustly passive for all admissible uncertainties. Additionally, for the passification problem, a delay-dependent sufficient condition is proposed in the form of strict linear matrix inequality (LMI), which not only removes the equality constraint but also makes the SMC gain matrix K solvable. Then a novel adaptive SMC law, which does not need to use the assumption that bounds of nonlinear perturbation function and external disturbance are known constants, is synthesized such that the finite-time reachability can be guaranteed. And the state information before and after state augmented transformation is utilized in SMC law design to help achieve better performance. Finally, four examples are presented to illustrate the effectiveness, superiority, and less conservativeness of the proposed scheme.

Stabilizer design for an under-actuated autonomous underwater vehicle in a descriptor model under unknown time delay and uncertainty

“…In the past two decades, descriptor (singular) systems that stemmed from singular perturbation theory concepts, also known as generalized state-space systems, have played a unique and significant role in complicated system modelling. They can describe physical systems better than regular ones (Liu et al, 2020). These systems are also referred to by other names, such as singular systems, semi-state systems, implicit systems, and algebraic-differential systems.…”

Passivity‐based stochastic sampled‐data control of Markovian jump systems via looped‐functional approach

“…The passivity analysis and design of control systems have attracted enormous attention. [6][7][8][9][10][11] References 6,7 carried out the passivity analysis of delayed neural networks. References 9,10 addressed the passivity-based sampled-data control for MJSs with aperiodic sampling.…”